Electric Charges and Fields.pdf for class 12 physics

ELECTROSTATICS: ELECTRIC CHARGES AND FIELD
Electrostatics is the study of charges at rest.
Charge (q)
- Charge is an intrinsic property of matter due to which it experiences Electrostatic forces of attraction and repulsion.
- There are two types of charges; positive (e.g. proton) and negative (e.g. electron)
- Charge on a single electron is e = 1.6 × 10-19
C | SI Unit- Coulomb(C)
Properties of charge
1. Attraction and repulsion: Like charges repel each other | Unlike charges attract each other
2. Additive nature of charge: Charge is additive in nature i.e. total charge on a body is the algebraic sum of all charges
present on the body.
Ques: Total charge on body = +10C +5C -3C-2C
= 10C Ans.
3. Quantisation of charge
- Charge on a body is the integral multiple of charge on a single Electron.
i.e. Q = ne
Where e is the charge on a single electron and n
Ques: Calculate the no. of electrons in 1C charge
Ans: q= ne; 1= n × 1.6×10-19
;;n= 6.25 × 1018
electrons.
4. Invariability of charge
- Charge is invariable in nature i.e. the charge on a body does not depend on its state of rest or motion.
Principle of conservation of charge
In an isolated s stem charge can neither be created nor destro ed
Note: If a body has excess electrons, it has a negative charge.
If a body has excess protons, it has a positive charge.
Methods of charging bodies
1. Charging bodies by rubbing/friction
When two bodies are rubbed together, the friction between the bodies causes transfer of electrons from one body
to another and as a result both bodies become charged. The body which loses electrons becomes positively charged
and the body which gains electrons becomes negatively charged.
Eg - rubbing glass rod with silk, rubbing plastic rod with fur
- By convention, charge on glass rod and fur is positive and charge on silk cloth and plastic rod is negative.
a.
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T ① ← →
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mas '
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-

ELECTROSTATICS: ELECTRIC CHARGES AND FIELD
Electrostatics is the study of charges at rest.
Charge (q)
- Charge is an intrinsic property of matter due to which it experiences Electrostatic forces of attraction and repulsion.
- There are two types of charges; positive (e.g. proton) and negative (e.g. electron)
- Charge on a single electron is e = 1.6 × 10-19
C | SI Unit- Coulomb(C)
Properties of charge
1. Attraction and repulsion: Like charges repel each other | Unlike charges attract each other
2. Additive nature of charge: Charge is additive in nature i.e. total charge on a body is the algebraic sum of all charges
present on the body.
Ques: Total charge on body = +10C +5C -3C-2C
= 10C Ans.
3. Quantisation of charge
- Charge on a body is the integral multiple of charge on a single Electron.
i.e. Q = ne
Where e is the charge on a single electron and n
Ques: Calculate the no. of electrons in 1C charge
Ans: q= ne; 1= n × 1.6×10-19
;;n= 6.25 × 1018
electrons.
4. Invariability of charge
- Charge is invariable in nature i.e. the charge on a body does not depend on its state of rest or motion.
Principle of conservation of charge
In an isolated s stem charge can neither be created nor destro ed
Note: If a body has excess electrons, it has a negative charge.
If a body has excess protons, it has a positive charge.
Methods of charging bodies
1. Charging bodies by rubbing/friction
When two bodies are rubbed together, the friction between the bodies causes transfer of electrons from one body
to another and as a result both bodies become charged. The body which loses electrons becomes positively charged
and the body which gains electrons becomes negatively charged.
Eg - rubbing glass rod with silk, rubbing plastic rod with fur
- By convention, charge on glass rod and fur is positive and charge on silk cloth and plastic rod is negative.
a.
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T ① ← →
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-
( PYQ 2021,20,18,17 )
(Removed for 2023-24)

2. Charging by touch
When a charged body is made to touch an uncharged body, some of the charge from the charged body is
transferred to the other body. This is called charging by touch.
3. Charging by induction
Let us understand charging by induction through an example.
- Take two metallic spheres A and B (mounted on insulating stands) and bring them together.
- Now, bring a positively charged rod near the left end of sphere A (not touching).
- The positive charge of the rod attracts the electrons of A as a result there is an excessive negative charge on left side
of A. At the same time, there is an accumulation of excessive positive charge on right side of sphere B due to
repulsive forces.
- So, we see that at the end of this process, both spheres become charged. This process of charging is called charging
by induction.
Note: 1. Charges on both spheres will be equal and opposite.
2. Not all the electrons in the sphere accumulate on one side because as electrons keep getting accumulated, the
incoming electrons feel a strong force of repulsion from the already accumulated electrons. Over time equilibrium is
set up under the force of attraction of the rod and force of repulsion of the electrons.
Gold leaf Electroscope
- Used to detect charge on a body.
Working: when a charged body is brought near or touched with
the metal knob, charge travels to the leaves through the rod.
Since both the leaves have the same charge they diverge(repel)
The degree of divergence is an indicator of amount of charge.
i
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Co lomb La (PYQ 2019, 2014, 2011)
The magnitude of electrostatic force between two point objects is directly proportional to the product of the two
charges and inversely proportional to the square of the distance between them and acts along the line joining their
centres.
PERMITTIVITY OF FREE SPACE (H )
H =8.85×10-12
C2
N-1
m-2
PERMITTIVITY IN MEDIUM (H)
There exists a relation between permittivity in free space/vacuum and that in a medium.
Hr = K = H/H , where Hr is the relative permittivity of medium AKA K ( dielectric constant of medium)
Ques: Plot a graph showing variation of coulomb force (F) versus 1/r2
, where r is the distance between the two charges
of each pair of charges A(1µC,2µC) and B (1µC, -3µC) (PYQ 2011)
soln
: We know F v 1/r2
, therefore, Similar PYQs
ques: A thin metallic spherical shell of radius R
carries a charge Q on its surface. A point charge
Q/2 is placed at its center C and another charge
+2Q is placed at a distance x from the center.
Find force on the charge Q/2 and 2Q. (PYQ 2015)
Since F v q1q2 , graph for pair B will have greater slope
Than slope of pair A.
Force between multiple charges
Principle of superposition
Principle of superposition talks about two things
1. Net force on any charge is the vector sum of all the forces acting on that charge
2. The individual forces between two charges are unaffected due to the presence of other charges
Hint: field
inside shell is
zero
II
t
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.

Ques:
Soln
In ABC e can calculate
AO=BO=CO= l/2 ÷ cos30 l
Now, let us calculate the forces between the three charges at the vertices and charge Q at the centroid individually
(principle of superposition)
F1 =3kq1Q/l2
(-ĵ
F2= 3kq1Q/l2
sin î cos ĵ
F3= 3kq1Q/l2
(-sin î cos ĵ
Now to calculate net force on Q we find the vector sum of the forces F1 + F2 + F3 which amounts to zero.
We can also see by symmetry that net force on Q is zero.
Electric Field
Electric field can be defined as the space around a charge in which another charge experiences an electrostatic force of
attraction and repulsion An electric charge Q produces an electric field ever here in its surrounding.
Electric field strength/ field intensity (E)
- Electric field strength at a point is defined as the force that a unit charge experiences when kept at that point.
- Mathematically , lim qo0 E=F/q
- It is a vector quantity | SI Unit- N/C or V/m
General expression for field strength:
Let us take a charge Q. at a distance r from it, there is another unit charge q. the force on q due to Q can be written
as-
F = k Q.q/r2
E = F/q
E = k Q/r2
Note: Electric field strength also follows law of superposition i.e. net electric field strength at a point is the vector
sum of all field strengths due to individual charges.
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Characteristics of Electric field
1. Electric field at a point doesn t depend on charge q as the ratio F/q is independent of q.
2. For a positive point charge electric field is directed radially outwards.
3. For a negative point charge electric field is directed radially inwards.
4. Magnitude of E due to a charge Q depends inversely on R2
, so at equal distances from the charge Q, E will have same
magnitude i.e. it shows radial symmetry.
Ques: A charge is uniformly distributed over a ring of radius a. Obtain an expression for the electric field at its center.
Hence show that for large distances it behaves like a point charge. (PYQ 2016)
Ans.
Similar PYQs
Electric Field lines (PYQ 2020,2019,2018,2017,2016,2015,2014,2013,2012,2011,2010)
- The concept of electric field lines was given by Faraday to visualise the strength of electric fields.
- Electric field lines are imaginary, straight or curved lines around charged bodies such that tangent to it at a point
gives direction of electric field at that point.
Properties of Electric Field lines
1. Field lines originate from a positive charge and terminate at a negative charge.
Consider a differential
Element of length dl
And charge dq
Field along x-axis
Field along y-axis
(Due to symmetry)
So, field at center
Intersect
each other
*le Electric ﬁeld lines
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2. Two field lines can never intersect each other. (This is because at the point of intersection we can draw two tangents
which means electric field at the point of intersection will have two directions, which is not possible.)
3. Greater is the density of field lines, greater is the strength of electric field in the region
4. Electrostatic field lines do not form closed loops because of the conservative nature of electric field (i.e. work done
by electric field depends on final and initial position and not the path followed.)
5. Electric field lines do not have any breaks; they are continuous in nature.
Ques: Draw pattern of electric field lines, when a point charge Q is kept near an uncharged conducting plate. (PYQ
2019)
Ans.
Electric Dipole
An electric dipole is an arrangement of 2 equal and opposite charges kept at some finite distance.
Dipole Moment (P)
- The dipole moment (vector quantity) of an electric dipole measures the strength of the dipole
- Its magnitude is equal to the product of the charge and the separation between the two charges
P = q.(2l)
- Its direction is along the dipole axis, from the negative charge to the positive charge.
Electric field due to dipole (PYQ 2019,2018,2017,2016,2015,2011)
A. Field on axial positon/ End on position (PYQ 2015)
Strong field
Weak field
For r
(PYQ)
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B. Electric field on equatorial position/ Broad on position (PYQ 2017)
Ques: what is the expression for the electric field produced by a dipole of moment p at a point at a distance r in the
equatorial plane? Draw a E v/s r graph for the same (PYQ 2015)
Ans:
Similar PYQs
ques: a) derive an expression for the electric field at the equatorial line for a dipole
b) Two identical point charges, q each are kept 2m apart in air. A third point charge Q of unknown magnitude and sign is
placed on the lone joining the charges such that system remains in equilibrium. Find the position and nature of Q.
(PYQ 2019)
Behaviour of dipole in external electric field
Let us assume that a dipole of dipole moment P is kept in a uniform external field E at an angle T with the field.
As we can see from the figure, the net force on the dipole will be zero. But since line of action of the two forces is not
the same, the dipole will experience a torque W which can be written as,
Field along x-axis
For d >> l
Field along y axis
(Hint: ﬁeld will be 0 in b/w the
charges, on the line joining
them)
rise
cos.
Imo i
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,
l l
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- From this we can see that net torque on the dipole is zero when it makes an angle of 0°(parallel) or 180°(anti-
parallel) with the field.
- When the dipole is parallel to the field, it is known as the position of stable equilibrium and when it is anti-parallel, it
is known as the position of unstable equilibrium.
- The torque on the dipole is maximum when it is perpendicular to the field.
Dipole in non-uniform electric field
In a non-uniform field, the two charges +q, -q experience different forces therefore net force is not zero.
The net torque may or may not be zero depending upon the orientation of the dipole.
Electric Flux (I)
Electric flux can be defined as the number of field lines crossing per unit area, perpendicular to it.
Mathematically,
I = E.A
= EAcosT (Where E is the field vector and A is the area vector)
Note: the direction of the area vector is along the normal to the area.
Ques: Given a uniform electric field E = 5 ×103
î N/C. Find flux of this field through a square of side 10cm whose plane is
parallel to the y-z plane. What would be the flux through the same square if its plane makes an angle of 30° with the x-
axis? (PYQ 2014)
Ans: 1) I= E A cosT
= 5 × 103
× 10-2
cos0° = 50 NC-1
m2
2) Since plane makes angle of 30°, normal will make angle of 90-30= 60°
I=E A cosT = 5 × 103
× 10-2
cos60°= 25 NC-1
m2
Ga La (PYQ 2019,2018,2017,2016,2014)
Total electric flu through a closed surface is equal to 1/H times the total charge enclosed b the closed surface
I = ∮E.ds=q/H˳
Derivation:
Let us assume a sphere of radius r which encloses charge q. Consider differential area ds. The flux through ds can be
written as,
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( PYQ 2021,19,18,16 )
( PYQ 2022,21,20,19,18 )

Note: if net charge enclosed by a surface is zero, then the net flux through that surface is also zero (since I=q/H ).
Impo an poin ega ding Ga la
- Gauss la is true for an closed surface irrespective of its shape
- The term q on the right side of the equation refers to all the charges inside the closed surface.
- The term E on the left side is due to all charges both inside and outside the surface.
- The closed surface is called Gaussian surface and it cannot pass through a point charge (can pass through continuous
charge)
- Gauss la is based on inverse square dependence on distance as seen in coulomb s la . Any violation of gauss law
will result in departure from the inverse square law.
Ques: Consider two hollow concentric spheres, S1 and S2 (S2>S1) enclosing charges 2Q and 4Q resp. Find the ratio of
flux through them. How will the flux through S1 change if a medium of dielectric constant k is introduced in S1? (PYQ
2014)
Ans:
According to gauss law, I= q/H
1) I1= 2Q/H ; I2= 6Q/H
I1/I2 =1/3
2) If a medium of dielectric const K is introduced in S1
H= kH
I1 = 2Q/kH
Similar PYQs
(According to gauss law)
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KIN
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Qm÷sed
( PYQ 2020 , Ans A )

Application of Ga La
I) Field due to an infinitely long straight uniformly charged wire (PYQ 2017)
Consider an infinite straight wire with uniform charge density , draw a cylindrical Gaussian surface of radius r and
length l around it.
Important PYQ
II) FIELD DUE TO UNIFORMLY CHARGED PLANE SHEET (PYQ 2017)
Consider an infinite plane sheet with uniform charge density , draw a cylindrical Gaussian surface of radius r and length
2l as shown.
also,
Equating 1,2
,
⇐
e ,
⇐
( " Ets .E
y
,
÷
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i÷•zg¥BBa
←
⇐ ⇐
( PYQ 2021,20,17)
( PYQ 2016)

Important PYQ
III) FIELD DUE TO A UNIFORMLY CHARGED THIN SPHERICAL SHELL (PYQ 2020)
Consider a uniformly charged spherical shell of radius r with uniform charge density , draw a spherical Gaussian surface
of radius x
Case 1: x > r
Consider the Gaussian surface at a distance x (from centre) outside the sphere
also,
Equating 1,2
According to Gauss’s law
also,
Equating 1,2
For x=r
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Case 2: x < r
Consider the Gaussian surface inside the sphere. As shown in the previous part
Charge enclosed in this Gaussian surface is 0 therefore,
Ques: A hollow cylindrical box of length 1m and area of cross-section 25 cm2
is placed in a three dimensional coordinate
system as shown in the figure. The electric field in the region is given by E = 50x î, where E is in NC-1
and x is in meters.
Find
i) Net flux through the cylinder
ii) Charge enclosed by the cylinder (PYQ 2013)
Ans:
Important PYQ
( PYQ 2013 )
( PYQ 2018 )
( PYQ 2020)

SoLuTiOnS fOr sImIlAr PyQS
Ans 1. PYQ 2015 soln
A. Force on Q/2
(Field inside conductor is 0)
B. Force on 2Q
Ans 2. PYQ 2018 soln
Ans3. PYQ 2019 soln
Nature is positive (see fig)
Ans4. PYQ 2016 soln
According to gauss law,
Since charge enclosed remains same, flux doesn’t
change.
Ans5. PYQ 2018 soln
Ans6. PYQ 2020 soln
ET
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1 .
Electric Charges and Fields
1. Draw the pattern of electric field lines, when a point charge –Q is kept near an uncharged
conducting plate. [CBSE DELHI 2019]
Ans.
+
–Q
+ + + –
–
–
–
[Note: (i) Deduct ½ mark, if arrow are not shown.
(ii) Do not deduct any mark, if charges on the plates are not shown.
1 1
2. Define electric flux. Is it a scalar or a vector quantity. [CBSE DELHI 2018]
Ans. (a) Electric flux through a given surface is defined as the dot
product of electric field and area vector over that surface.
Alternatively
s
E . dS
o o
I ³
Also accept
Electric flux, through a surface equals the surface integral of the
electric field over that surface.
It is a scalar quantity.
½
½
1
3. Write two properties by which electric potential is related to the electric field.
[CBSE DELHI COMPARTMENT 2017]
Ans. (i) Electric field is in the direction in which potential decreases at
the maximum rate.
(ii) Magnitude of electric field is given by change in the magnitude
of potential per unit displacement normal to a charged conducting
surface.
[Alternatively: award half mark of part ‘a’ if student writes only
dV
E
dr
]
½
½
1

2 .
4. How does the electric flux due to a point charge enclosed by a spherical Gaussian surface
get affected when its radius is increased? [CBSE DELHI 2016]
Ans. Electric flux remains unaffected.
[Note: (As per the Hindi translation), change in Electric field is
being asked, hence give credit if student writes answer as decreases]
1 1
5. What is the electric flux through a cube of side 1 cm which encloses an electric dipole?
[CBSE DELHI 2015]
Ans. In a cubic surface, the net electric charge will be zero since dipole
carries equal and opposite charges. It is observed that the net electric
flux through closed surface will be [Charge enclosed / ε₀] and
because the charge enclosed is zero. Electric flux is also zero.
1 1
6. Why should electrostatic field be zero inside a conductor? [CBSE DELHI 2012]
Ans. For a charged conductor, the charges will lie on the surface of the
conductor. So, there will not be any charges inside the conductor.
When there is no charge there will not be electric field.
1 1
7. If the net electric flux through a closed surface is zero, then we can infer
(a) no net charge is enclosed by the surface
(b) uniform electric field exists within the surface.
(c) electric potential varies from point to point inside the surface.
(d) charge is present inside the surface. [CBSE DELHI 2020]
Ans. (a) No net charge is enclosed by the surface.
Explanation:
1. Net electric flux is directly proportional to the net electric
charge enclosed by the surface.
2. In a closed surface, if the net electric flux is zero, then the net
electric charge will also be zero.
3. Since electric flux is defined as the rate of flow of electric field
in a closed area and if the electric flux is zero the overall
electric charge within the closed boundary will also be zero.
1 1
8. Draw a plot showing the nature of variation of the Electric field (E) and potential (V), of a
(small) electric dipole with the distance (r) of the field point from the centre of the dipole.

3 .
Ans. Electric potential Electric Field
0
Q 1
V ; i.e., V
4 r r
v
SH 2 2
0
Q 1
E ; i.e., E
4 r r
v
SH
The graph below shows us the variation of E and V with distance
‘r’.
½
½
1
9. A charge q is placed at the point of intersection of body diagonals of a cube. Electric flux
passing through any one of its face.
Ans.
Charge is placed at the point of intersection of body diagonal of a
cube which means charge placed a the centre of cube.
According to Gauss theorem, the electric flux through the whose
cube is given by
0
q
H
· Since, a cube has total 6 faces, the flux will be
divided equally among those 6 faces each will receive
1
6
th of the
total flux. So the required flux will be
0
q
6H
·
1 1
10. A point positive charge is brought near a isolated conducting sphere. Which of the
following figure correctly shows the electric field lines.

4 .
Ans. (i) is the correct answer
x The electrical lines move from positive charge to negative
charge.
x When positive charge is brought near conducting sphere from
left side then negative charges are formed on the left side and
equal amount of positive charges are formed on right side on
conducting sphere.
x The electrical lines from positive charges flow from positive to
negative and the electrical lines are emanate from positive
charges.
1 1

Directions: These questions consist of two statements, each printed as Assertion and Reason.
While answering these questions, you are required to choose any one of the following four
responses.
(A) If both Assertion and Reason are correct and the Reason is a correct explanation of the Assertion.
(B) If both Assertion and Reason are correct but Reason is not a correct explanation of the Assertion.
(C) If the Assertion is correct but Reason is incorrect.
(D) If both the Assertion and Reason are incorrect.
1. Assertion (A): If proton and an electron are placed in the same uniform electric field
experience forces of different magnitudes.
Reason (R): Electrostatic force on a charge is independent of mass.
2. Assertion (A): The Coulomb force is the strongest force in the universe.
Reason (R): Nuclear forces are weaker than Coulomb force.
3. Assertion (A): In a non-uniform electric field, a dipole will have translatory as well as
rotatory motion.
Reason (R): In a non-uniform electric field, a dipole experiences a force as well as torque.
4. Assertion (A): The coulomb force is the dominating force in the universe.
Reason (R): Coulomb force is weaker than gravitational force.
5. Assertion (A): Electric lines of force cross each other.
Reason (R): The resultant electric field at a point is the superimposition of the electric
fields at that point.
6 . Assertion (A): Gauss theorem is not applicable in magnetism.
Reason (R): Magnetic mono pole do not exist.
7. Assertion (A): If two spherical conductors of different radii have the same surface
charge densities their electric field intensities will be equal.
Reason (R): Surface charge density (Total charge) / area.
[CBSE Marking Scheme, 2021]
(E) If Assertion is
wrong
Reason is correct
-

FARADAY CAGE:
A Faraday cage or Faraday shield is an enclosure made of a conducting material. The
fields within a conductor cancel out with any external fields, so the electric field within
the enclosure is zero. These Faraday cages act as big hollow conductors you can put
things in to shield them from electrical fields. Any electrical shocks the cage receives,
pass harmlessly around the outside of the cage.
1. Which of the following material can be used to make a Faraday cage?
(a) Plastic
(b) Glass
(c) Copper
(d) Wood
2. Example of a real-world Faraday cage is
(a) Car
(b) Plastic box
(c) Lightning rod
(d) Metal rod
3. What is the electrical force inside Faraday cage when it is struck by lightning?
(a) The same as the lightning
(b) Half that of the lightning
(c) Zero
(d) A quarter of the lightning
Electric Charges and Fields
CASE STUDY 1:

4. An isolated point charge q is placed inside the Faraday cage. Its surface must have
charge equal to
(a) Zero
(b) +q
(c) -q
(d) +2q
5. A point charge of 2C is placed at centre of Faraday cage in the shape of cube with
surface of 9 cm edge. The number of electric field lines passing through the cube
normally will be
a) 1.9105 Nm2 /C entering the surface
b) 1.9105 Nm2 /C leaving the surface
c) 2.0105 Nm2 /C leaving the surface
d) 2.0105 Nm2 /C entering the surface
CASE STUDY 2:
Electric field strength is proportional to the density of lines of force i.e, electric field
strength at a point is proportional to the number of lines of force cutting a unit area
element placed normal to the field at that point. As illustrated in given figure, the
electric field at P is stronger than at Q

(i) Electric lines of force about a positive point charge are
(a) radially outwards
(b) circular clockwise
(c) radially inwards
(d) parallel straight lines
(ii) Which of the following is false for electric lines of force?
(a) They always start from positive charge and terminate on negative charges.
(b) They are always perpendicular to the surface of a charged conductor.
(c) They always form closed loops.
(d) They are parallel and equally spaced in a region of uniform electric field.
(iii) Which one of the following patterns of electric line of force is not possible in
field due to stationary charges?
(iv) Electric field lines are curved
(a) in the field of a single positive or negative charge
(b) in the field of two equal and opposite charges.
(c) in the field of two like charges.
(d) both (b) and (c)

(v) The figure below shows the electric field lines due to two positive charges. The
magnitudes EA, EB and Ec of the electric fields at point A, B and C respectively are
related as
(a) E E E
(b) E E E
(c) E = E E
(d) E E = E
A B C
B A C
A
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Electric Charges and Fields.pdf for class 12 physics

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